486 
DIOPHANTUS OF ALEXANDRIA 
I. 12. x x + x 2 = y x + y 2 — a, x x = my 2 , y x = nx 2 (x x >x 2 , y x >y 2 ). 
I x x = my 2 , y x = nz 2 , z x - px 2 ) 
I. 15. x + a = m(y — a), y + b = n{x—b). 
[Diophantus puts y = £ + a, where £ is his unknown.] 
1.16. y + z = a, z + x=h, x + y = c. [Dioph. puts £ =x + y + z.] 
-I. 17. y + 0 + w = a, z + w + x = b, w + x + y = c, x + y + z = cl. 
[x + y + z + w = £.] 
I. 18. y + Z — X — a, z + x — y — b, x + y — z = c. 
[Dioph. puts 21 = x + y + z.\ 
I. 19. y + z + w — x = a, z+w+x— y — b, w + x + y — z = c, 
x + y + z — w = d. 
[2£ = x + y + z + w.~] 
I. 20. x + y + z = a, x + y — mz, y + z = nx. 
I. 21. x = y + — z, y = z+ ~x, z = a + - y (where x>y>z), 
m n v 
with necessary condition. 
\m / \p / ■ \n / Vm 
(iii) Determinate systems of equations reducible to the 
first degree. 
I. 26. ax = a 2 , = a. 
I. 29. x + y = a, x? — y 2 — b. [Dioph. puts 2£ = œ-y.] 
/1. 31. x = my, x 2 + y 2 = n(x + y). 
I. 32. x = my, x 2 + y 2 = n{x — y). 
I. 33. a; = my, x? — y l — n{x + y). 
(l. 34. a; = my, x 2 —y 2 = n{x — y). 
I. 34. Cor. 1. œ = my, xÿ = %(ic + y). 
t Cor. 2. x = my, xy = n{x — y).